メモ ”He and others went on to show that higher order logic was beautifully captured in the setting of category theory (more specifically toposes).” https://math.mit.edu/~dspivak/ David Spivak Research Scientist Department of Mathematics MIT https://ocw.mit.edu/courses/mathematics/18-s996-category-theory-for-scientists-spring-2013/# Category Theory for Scientists MIT OpenCourseWare, Massachusetts Institute of Technology https://ocw.mit.edu/courses/mathematics/18-s996-category-theory-for-scientists-spring-2013/textbook/ Category Theory for Scientists Textbook https://math.mit.edu/~dspivak/CT4S.pdf Category Theory for Scientists (Old Version) David I. Spivak September 17, 2013
P10 Bill Lawvere saw category theory as a new foundation for all mathematical thought. Mathematicians had been searching for foundations in the 19th century and were reasonably satisfied with set theory as the foundation. But Lawvere showed that the category of sets is simply a category with certain nice properties, not necessarily the center of the mathematical universe. He explained how whole algebraic theories can be viewed as examples of a single system. He and others went on to show that higher order logic was beautifully captured in the setting of category theory (more specifically toposes). It is here also that Grothendieck and his school worked out major results in algebraic geometry.
